Is God a Mathematician?

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by Lord Byron. The phrase was apparently the culmination of Archimedes’ investigations into the problem of moving a given weight with a given force. Plutarch tells us that when King Hieron asked for a practical demonstration of Archimedes’ ability to manipulate a large weight with a small force, Archimedes managed—using a compound pulley—to launch a fully loaded ship into the sea. Plutarch adds in admiration that “he drew the ship along smoothly and safely as if she were moving through the sea.” Slightly modified versions of the same legend appear in other sources. While it is difficult to believe that Archimedes could have actually moved an entire ship with the mechanical devices available to him at the time, the legends leave little room for doubt that he gave some impressive demonstration of an invention that enabled him to maneuver heavy weights.
    Archimedes made many other peacetime inventions, such as a hydraulic screw for raising water and a planetarium that demonstrated the motions of the heavenly bodies, but he became most famous in antiquity for his role in the defense of Syracuse against the Romans.
    Wars have always been popular with historians. Consequently, the events of the Roman siege on Syracuse during the years 214–212 BC have been lavishly chronicled by many historians. The Roman general Marcus Claudius Marcellus (ca. 268–208 BC), by then of considerable military fame, anticipated a rapid victory. He apparently failed to consider a stubborn King Hieron, aided by a mathematical and engineering genius. Plutarch gives a vivid description of the havoc that Archimedes’ machines inflicted upon the Roman forces:
    He [Archimedes] at once shot against the land forces all sorts of missile weapons, and immense masses of stone that came down with incredible noise and violence; against which no man could stand; for they knocked down those upon whom they fell in heaps, breaking all their ranks and files. At the same time huge poles thrust out from the walls over the ships sunk some by great weights which they let down from on high upon them; others they lifted up into the air by an iron hand or beak like a crane’s beak and, when they had drawn them up by the prow, and set them on end upon the poop, they plunged them to the bottom of the sea…A ship was frequently lifted up to a great height in the air (a dreadful thing to behold), and was rolled to and fro, and kept swinging, until the mariners were all thrown out, when at length it was dashed against the rocks, or let fall.
    The fear of the Archimedean devices became so extreme that “if they [the Roman soldiers] did but see a piece of rope or wood projecting above the wall, they would cry ‘there it is again,’ declaring that Archimedes was setting some engine in motion against them, and would turn their backs and run away.” Even Marcellus was deeply impressed, complaining to his own crew of military engineers: “Shall we not make an end of fighting against this geometrical Briareus [the hundred-armed giant, son of Uranus and Gaia] who, sitting at ease by the sea, plays pitch and toss with our ships to our confusion, and by the multitude of missiles that he hurls at us outdoes the hundred-handed giants of mythology?”
    According to another popular legend that appeared first in the writings of the great Greek physician Galen (ca. AD 129–200), Archimedes used an assembly of mirrors that focused the Sun’s rays to burn the Roman ships. The sixth century Byzantine architect Anthemius of Tralles and a number of twelfth century historians repeated this fantastic story, even though the actual feasibility of such a feat remains uncertain. Still, the collection of almost mythological tales does provide us with rich testimony as to the veneration that “the wise one” inspired in later generations.
    As I noted earlier, Archimedes himself—that highly esteemed “geometrical Briareus”—attached no particular significance to all of his military

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